where \({\tilde{\bf {H}}}\)  denotes the \(M\times N\)  angular cascaded channel, \({\bf {U}}_{M}\)  and \({\bf {U}}_{N}\)  are the \({M \times M}\)  and \({N \times N}\)  dictionary unitary matrices at the BS and the RIS, respectively. The number of non-zero elements in \({\tilde{\bf {H}}}\)  is determined by the product of the number of paths between the RIS and the BS and that between the user and the RIS. Since there are the limited number of scatters around the BS and the RIS, especially in high-frequency communications, \({\tilde{\bf {H}}}\)  is usually sparse in nature [1]}, as shown in Fig. 3.
<FIGURE>